A NOTE ON MONOTONE CONVERGENCE TO SOLUTIONS OF FIRST ORDER DIFFERENTIAL EQUATIONS
RAND CORP SANTA MONICA CA
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The purpose of this brief note was to show that one can obtain a monotone increasing sequence of approximations to the solution of the differential equation dudt phiu,t, uo c, provided that one assume that phiu,t is a twice differentiable convex function of u in some t-interval o,t sub 0. Similarly, monotone decreasing sequences can be obtained if phi is concave.
- Theoretical Mathematics